Question

Write the solution of each inequality in set-builder notation.3(2k + 12) < -42

Answer 1

`\lbrace k|k\in R,k<-13\rbrace`

EXPLANATION :

From the given inequality :

`3(2k+12)<-42`

Simplify and solve the values of k.

`\begin{gathered} 3(2k+12)<-42 \\ 6k+36<-42 \\ 6k<-42-36 \\ 6k<-78 \\ k<-(78)/(6) \\ k<-13 \end{gathered}`

The solution is all real numbers that are less than -13

In set builder notation :

`\mleft\lbrace k|k\in R,k<-13\mright\rbrace`